Surface-Collision Analysis of Microscale-Confined ¹²⁹Xe in Pyrex Vapor Cells Based on Stem-Transport and Gradient...

Surface collisions at Pyrex walls limit the spin coherence in nuclear magnetic resonance gyroscopes (NMRG) vapor cells, while the cavity-stem junction introduces geometry dependent exchange that perturbs the transverse spin relaxation time T2 of ¹²⁹Xe atoms. We combine T2 measurements with Monte Carlo simulations of confined diffusion and surface collisions to decompose the relaxation of Xe atoms and derive a cavity-stem geometry correction for wall relaxation. A structural coupling factor (SCF) is introduced to compress stem length and aperture diameter into a dimensionless metric for diffusion-limited mixing, enabling prediction of the transverse relaxation rate versus geometry. Across eight simulated configurations, the model yields R2=0.982 and agrees with experiments within 7-9%, comparable to the measurement uncertainty (±0.015s-1). Using the validated framework, geometry optimization reduces the relaxation rate from 0.225 to 0.131s-1 (a 41.8% improvement). This Pyrex surface-collisional analysis provides an in-situ, T2-based route to compare effective surface depolarization across fabrication and surface-treatment protocols while accounting for cavity-stem coupling.